我还没有找到任何关于如何将给定的方程式向左对齐的明确指示。它会自动向右对齐,我尝试过在 split 旁边使用 {ll},但毫无用处:
\begin{equation}
\begin{split}
\alpha_k=\frac{1}{\pi}\sum_{i=0}^n\eta_i\int_{\xi_i}^{\xi_{i+1}} \cos kt \text{d}t=-\frac{1}{\pi}\sum_{i=0}^n\eta_i\bigg( \frac{\sin (k\xi_{i+1})}{k}-\frac{\sin (k\xi_{i})}{k}\bigg)=\\ \frac{1}{\pi}\sum_{i=0}^n\frac{\eta_i}{k}\big[\sin(\xi_i)-\sin(\xi_{i+1})\big]\rightarrow \text{let \ }\delta=\xi_i\\
\alpha_k=\frac{1}{\pi}\sum_{i=1}^n\frac{\eta_i}{k}\big[\sin\delta-\sin\gamma\big]\rightarrow \\
\alpha_k=\frac{1}{\pi}\sum_{i=1}^n\frac{\eta_i}{k}
\end{split}
\end{equation}
关于如何将其左对齐,有什么提示吗?
谢谢
更新,我得到了以下建议:
我改回原来的版本并添加了一些文字,但格式仍然相同,因此出现同样的问题:
\begin{equation}
\begin{split}
\alpha_k=\frac{1}{\pi}\sum_{i=0}^n\eta_i\int_{\xi_i}^{\xi_{i+1}} \cos kt \text{d}t=-\frac{1}{\pi}\sum_{i=0}^n\eta_i\bigg( \frac{\sin (k\xi_{i+1})}{k}-\frac{\sin (k\xi_{i})}{k}\bigg)=\\ \frac{1}{\pi}\sum_{i=0}^n\frac{\eta_i}{k}\big[\sin(k\xi_i)-\sin(k\xi_{i+1})\big]\rightarrow \text{let \ }\delta=\xi_i,\text{and \ }\gamma=\xi{_i+1}\\
\alpha_k=\frac{1}{\pi}\sum_{i=1}^n\frac{\eta_i}{k}\big[\sin k\delta-\sin k\gamma\big]\rightarrow \text{apply the relation}
\sin(\alpha+\beta)-\sin(\alpha-\beta)=2\sin\beta\cos\alpha\\
\text{let\ }\alpha=\frac{\delta+\gamma}{2}\text{\ and \ } \frac{\delta-\gamma}{2}=2\sin\frac{\delta+\gamma}{2}\cos\frac{\delta-\gamma}{2} \text{\, then obtain:}\\ \alpha_k=\frac{2}{\pi}\sum_{i=1}^n\frac{\eta_i}{k}\sin k\bigg(\frac{\xi_{i+1}-\xi_i}{2}\bigg)\cos k\bigg(\frac{\xi_i+\xi_{i+1}}{2}\bigg)
\end{split}
\end{equation}
答案1
您想要设置一个对齐点。
\documentclass{article}
\usepackage{amsmath}
\newcommand{\diff}{\mathop{}\!\mathrm{d}}% or just d, which I prefer
\begin{document}
Your attempt
\begin{equation}
\begin{split}
\alpha_k=\frac{1}{\pi}\sum_{i=0}^n\eta_i\int_{\xi_i}^{\xi_{i+1}} \cos kt \text{d}t=-\frac{1}{\pi}\sum_{i=0}^n\eta_i\bigg( \frac{\sin (k\xi_{i+1})}{k}-\frac{\sin (k\xi_{i})}{k}\bigg)=\\ \frac{1}{\pi}\sum_{i=0}^n\frac{\eta_i}{k}\big[\sin(\xi_i)-\sin(\xi_{i+1})\big]\rightarrow \text{let \ }\delta=\xi_i\\
\alpha_k=\frac{1}{\pi}\sum_{i=1}^n\frac{\eta_i}{k}\big[\sin\delta-\sin\gamma\big]\rightarrow \\
\alpha_k=\frac{1}{\pi}\sum_{i=1}^n\frac{\eta_i}{k}
\end{split}
\end{equation}
With alignment at the equals sign and with fixes
\begin{equation}
\begin{split}
\alpha_k &= \frac{1}{\pi}\sum_{i=0}^n\eta_i\int_{\xi_i}^{\xi_{i+1}}\cos kt \diff t
= -\frac{1}{\pi}\sum_{i=0}^n\eta_i \biggl(
\frac{\sin (k\xi_{i+1})}{k}-\frac{\sin (k\xi_{i})}{k}
\biggr)
\\
&= \frac{1}{\pi}\sum_{i=0}^n\frac{\eta_i}{k}\bigl[\sin(\xi_i)-\sin(\xi_{i+1})\bigr]
\rightarrow \text{let \ } \delta=\xi_i
\\
\alpha_k &= \frac{1}{\pi}\sum_{i=1}^n\frac{\eta_i}{k}\bigl[\sin\delta-\sin\gamma\bigr]
\rightarrow
\\
\alpha_k &= \frac{1}{\pi}\sum_{i=1}^n\frac{\eta_i}{k}
\end{split}
\end{equation}
\end{document}